相关论文: Adhesion and volume filling in one-dimensional pop…
We generalize the one-dimensional population model of Anguige \& Schmeiser [1] reflecting the cell-to-cell adhesion and volume filling and classify the resulting equation into the six types. Among these types, we fix one that yields a class…
We consider the Dirichlet problem for a compressible two-fluid model in three dimensions, and obtain the global existence of weak solution with large initial data and independent adiabatic constants \Gamma,\gamma>=9/5. The pressure…
We discuss several continuum cell-cell adhesion models based on the underlying microscopic assumptions. We propose an improvement on these models leading to sharp fronts and intermingling invasion fronts between different cell type…
We consider a linear size-structured population model with diffusion in the size-space. Individuals are recruited into the population at arbitrary sizes. The model is equipped with generalized Wentzell-Robin (or dynamic) boundary…
A class of parabolic cross-diffusion systems modeling the interaction of an arbitrary number of population species is analyzed in a bounded domain with no-flux boundary conditions. The equations are formally derived from a random-walk…
Marine species reproduce and compete while being advected by turbulent flows. It is largely unknown, both theoretically and experimentally, how population dynamics and genetics are changed by the presence of fluid flows. Discrete…
We develop and analyse a discrete, one-dimensional model of cell motility which incorporates the effects of volume filling, cell-to-cell adhesion and chemotaxis. The formal continuum limit of the model is a nonlinear generalisation of the…
In 2006 Armstrong, Painter and Sherratt formulated a non-local differential equation model for cell-cell adhesion. For the one dimensional case we derive various types of adhesive, repulsive, and no-flux boundary bonditions. We prove local…
A class of parabolic-parabolic Keller-Segel systems with degenerate diffusion and volume filling is studied in a bounded domain subject to no-flux boundary conditions. The equations are derived from a multiphase fluid model. The interplay…
The paper develops a hybrid method for solving a system of advection--diffusion equations in a bulk domain coupled to advection--diffusion equations on an embedded surface. A monotone nonlinear finite volume method for equations posed in…
A general class of cross-diffusion systems for two population species in a bounded domain with no-flux boundary conditions and Lotka-Volterra-type source terms is analyzed. Although the diffusion coefficients are assumed to depend linearly…
The spatio-temporal dynamics of a population present one of the most fascinating aspects and challenges for ecological modelling. In this article we review some simple mathematical models, based on one dimensional…
We develop a continuous mathematical model of population dynamics that describes the sequential emergence of new genotypes under limited resources. The framework models genotype density as a nonlinear flow in mutation space, combining…
In this paper, we study pattern formations in an aggregation and diffusion cell migration model with Dirichlet boundary condition. The formal continuum limit of the model is a nonlinear parabolic equation with a diffusivity which can become…
In this paper, a single population model with memory effect and the heterogeneity of the environment, equipped with the Neumann boundary, is considered. The global existence of a spatial nonhomogeneous steady state is proved by the method…
We consider a model system consisting of two reaction-diffusion equations, where one species diffuses in a volume while the other species diffuses on the surface which surrounds the volume. The two equations are coupled via a nonlinear…
In three space dimensions, we consider the compressible inviscid model describing the time evolution of two fluids sharing the same velocity and enjoying the algebraic pressure closure. By employing the technique of convex integration, we…
Cell-cell adhesion is an inherently nonlocal phenomenon. Numerous partial differential equation models with nonlocal term have been recently presented to describe this phenomenon, yet the mathematical properties of nonlocal adhesion model…
Global existence of very weak solutions to a non-local diffusion-advection-reaction equation is established under no-flux boundary conditions in higher dimensions. The equation features degenerate myopic diffusion and nonlocal adhesion and…
We are interested in the large-time behavior of solutions to finite volume discretizations of convection-diffusion equations or systems endowed with non-homogeneous Dirichlet and Neumann type boundary conditions. Our results concern various…